Optimising Tours for the Weighted Traveling Salesperson Problem and the Traveling Thief Problem: A Structural Comparison of Solutions

  • Jakob BossekEmail author
  • Aneta Neumann
  • Frank Neumann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12269)


The Traveling Salesperson Problem (TSP) is one of the best-known combinatorial optimisation problems. However, many real-world problems are composed of several interacting components. The Traveling Thief Problem (TTP) addresses such interactions by combining two combinatorial optimisation problems, namely the TSP and the Knapsack Problem (KP). Recently, a new problem called the node weight dependent Traveling Salesperson Problem (W-TSP) has been introduced where nodes have weights that influence the cost of the tour. In this paper, we compare W-TSP and TTP. We investigate the structure of the optimised tours for W-TSP and TTP and the impact of using each others fitness function. Our experimental results suggest (1) that the W-TSP often can be solved better using the TTP fitness function and (2) final W-TSP and TTP solutions show different distributions when compared with optimal TSP or weighted greedy solutions.


Evolutionary algorithms Traveling Thief Problem Node weight dependent TSP 



This work has been supported by the Australian Research Council (ARC) through grants DP160102401 and DP190103894, and by the South Australian Government through the Research Consortium “Unlocking Complex Resources through Lean Processing”.


  1. 1.
    Bischl, B., et al.: mlr: Machine learning in R. J. Mach. Learn. Res. 17(170), 1–5 (2016). Scholar
  2. 2.
    Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, W.R., Raghavan, P., Sudan, M.: The minimum latency problem. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 163–171 (1994)Google Scholar
  3. 3.
    Bonyadi, M.R., Michalewicz, Z., Barone, L.: The travelling thief problem: the first step in the transition from theoretical problems to realistic problems. In: 2013 IEEE Congress on Evolutionary Computation, pp. 1037–1044 (2013).
  4. 4.
    Bonyadi, M.R., Michalewicz, Z., Wagner, M., Neumann, F.: Evolutionary computation for multicomponent problems: opportunities and future directions. In: Datta, S., Davim, J.P. (eds.) Optimization in Industry. MIE, pp. 13–30. Springer, Cham (2019). Scholar
  5. 5.
    Bossek, J., Casel, K., Kerschke, P., Neumann, F.: The node weight dependent traveling salesperson problem: approximation algorithms and randomized search heuristics (2020). to appear at GECCO 2020Google Scholar
  6. 6.
    El Yafrani, M., Ahiod, B.: Population-based vs. single-solution heuristics for the travelling thief problem. In: Genetic and Evolutionary Computation Conference (GECCO), pp. 317–324. ACM (2016)Google Scholar
  7. 7.
    Faulkner, H., Polyakovskiy, S., Schultz, T., Wagner, M.: Approximate approaches to the traveling thief problem. In: Conference on Genetic and Evolutionary Computation (GECCO), pp. 385–392. ACM (2015)Google Scholar
  8. 8.
    Lawler, E.: The Travelling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, Hoboken (1985). Scholar
  9. 9.
    Mei, Y., Li, X., Yao, X.: On investigation of interdependence between sub-problems of the travelling thief problem. Soft Comput. 20(1), 157–172 (2016)CrossRefGoogle Scholar
  10. 10.
    Neumann, F., Polyakovskiy, S., Skutella, M., Stougie, L., Wu, J.: A fully polynomial time approximation scheme for packing while traveling. In: Disser, Y., Verykios, V.S. (eds.) ALGOCLOUD 2018. LNCS, vol. 11409, pp. 59–72. Springer, Cham (2019). Scholar
  11. 11.
    Polyakovskiy, S., Bonyadi, M.R., Wagner, M., Michalewicz, Z., Neumann, F.: A comprehensive benchmark set and heuristics for the traveling thief problem. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pp. 477–484. ACM (2014).
  12. 12.
    Reinelt, G.: TSPLIB-a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)CrossRefGoogle Scholar
  13. 13.
    Therneau, T., Atkinson, B.: rpart: recursive partitioning and regression trees (2018). R package version 4.1-13
  14. 14.
    Vitter, J.S., Flajolet, P.: Average-Case Analysis of Algorithms and Data Structures, pp. 431–524. MIT Press, Cambridge (1991)zbMATHGoogle Scholar
  15. 15.
    Wagner, M., Lindauer, M., Mısır, M., Nallaperuma, S., Hutter, F.: A case study of algorithm selection for the traveling thief problem. J. Heuristics 24(3), 295–320 (2017). Scholar
  16. 16.
    Wu, J., Polyakovskiy, S., Neumann, F.: On the impact of the renting rate for the unconstrained nonlinear knapsack problem. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pp. 413–419. ACM (2016).
  17. 17.
    Wu, J., Polyakovskiy, S., Wagner, M., Neumann, F.: Evolutionary computation plus dynamic programming for the bi-objective travelling thief problem. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pp. 777–784. ACM (2018).
  18. 18.
    Wu, J., Wagner, M., Polyakovskiy, S., Neumann, F.: Exact approaches for the travelling thief problem. In: Proceedings of the 11th International Conference on Simulated Evolution and Learning (SEAL), pp. 110–121 (2017)Google Scholar
  19. 19.
    Yafrani, M.E., Ahiod, B.: Efficiently solving the traveling thief problem using hill climbing and simulated annealing. Inf. Sci. 432, 231–244 (2018)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Optimisation and LogisticsThe University of AdelaideAdelaideAustralia

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